On the geometric Langlands conjecture

On the Geometric Langlands Conjecture

0.1. Background. Let X be a smooth, complete, geometrically connected curve over the finite field Fq. Denote by F the field of rational functions on X and by A the ring of adèles of F . The Langlands conjecture, recently proved by L. Lafforgue [Laf], establishes a correspondence between cuspidal automorphic forms on the group GLn(A) and irreducible, almost everywhere unramified, n–dimensional `...

Quantization of Hitchin’s integrable system and the geometric Langlands conjecture

This is an introduction to the work of Beilinson and Drinfeld [6] on the Langlands program. Mathematics Subject Classification (2000). Primary 11R39; Secondary 14D20.

Geometric Realization of Whittaker Functions and the Langlands Conjecture

1.1. Let X be a smooth, complete, geometrically connected curve over Fq. Denote by F the field of rational functions on X , by A the ring of adeles of F , and by Gal(F/F ) the Galois group of F . The present paper may be considered as a step towards understanding the geometric Langlands correspondence between n–dimensional `–adic representations of Gal(F/F ) and automorphic forms on the group G...

Lecture on Langlands Functoriality Conjecture

On the Conjecture of Langlands and Rapoport

FORENOTE (2007): The remarkable conjecture of Langlands and Rapoport (1987) gives a purely group-theoretic description of the points on a Shimura variety modulo a prime of good reduction. In an article in the proceedings of the 1991 Motives conference (Milne 1994, §4), I gave a heuristic derivation of the conjecture assuming a sufficiently good theory of motives in mixed characteristic. I wrote...